Jim taking out two bad guys at once in "The Night of the Human Trigger."
Artie's swordfight in "The Night of the Big Blast" - it takes place at a Mardi Gras party, with Artie dressed as Don Juan and his three opponents as musketeers, and rages from balcony to ballroom to staircase top.
The old Indian chief refusing to take any crap from Loveless in "The Night of the Green Terror" (bonus points for being the only person in the entire series to tell him to shut up - and Loveless shuts up!).
"The Night of the Big Blackmail" is possibly the series' best illustration of what a magnificent team Jim and Artie make. They're each incredibly skilled in their own areas, but it is their combined strength that allows them to pull off the near-impossible and save the day.
Count Manzeppi surely deserves a mention for a) managing to meet Jim and Artie on their own turf (i.e. the train) in both of his appearances and b) being the only villain to make multiple appearances who never gets caught!
The make-shift launching pad Jim and Artie make and use in "The Night of the Burning Diamond". Only Jim and Artie can make something out of a Looney Tunes skit look totally awesome.